Answer:
( 3 + 4i )
Step-by-step explanation:
For this problem, we need to know that i^2 = -1. With this, let's solve the multiplication problem.
So to get rid of the i, we know it needs to be squared. The question is, for the sun of the products do we have a -4i or a +4i? So we will test both.
( 3 - 4i )^2 ?= 25
( 3 - 4i )( 3 - 4i ) ?= 25
9 - 12i - 12i - 16 ?= 25
We can stop here since we know that 24i will never equal 25.
So let's try the -4i
( 3 + 4i )( 3 - 4i ) ?= 25
9 + 12i - 12i + 16 ?= 25
9 + 16 ?= 25
25 == 25
Thus, our term for this to be true is ( 3 + 4i ).
Cheers.
Melanie is going to invest $45,000 and leave it in an account for 20 years. Assuming
the interest is compounded continuously, what interest rate, to the nearest
hundredth of a percent, would be required in order for Melanie to end up with
$142,000?
Answer:
Rate of interest r = 5.20% (Approx.)
Step-by-step explanation:
Given:
Amount invested p = $45,000
Final amount A = $142,000
Number of year = 20
Find:
Rate of interest r
Computation:
A = p[1+r]ⁿ
142,000 = 45,000[1+r]²⁰
3.1556 = [1+r]²⁰
r = 5.194
Rate of interest r = 5.20% (Approx.)
What is the value of the discriminant? 3y2 = 8y + 2
−40
56
72
88
Answer:
88
Step-by-step explanation:
a = 3
b = -8
c = -2
(-8)² 4(3)(-2) = 64 + 24
Herschel Supply Co backpack costs $54.99. Take $15.00 off the original price. Calculate the percent you saved on the backpack. Round to the nearest percent.
Answer:
it is 67%
Step-by-step explanation:
im sure with that
3 minus the product of 2 and a number X
Answer:
3 - 2x
Step-by-step explanation:
[tex]\huge\bold\purple{3 - 2x}[/tex]
Write f(x) in terms of sin(x) and cos(x).
Answer:
f(x) = cos(x)
Step-by-step explanation:
Given the expression
[tex]tan(x)csc(c) = \frac{1}{f(x)}[/tex]
Recall that;
[tex]tan(x) = \frac{sin(x)}{cos(x)} \\csc(x) = \frac{1}{sin(x)} \\[/tex]
Substitute into the given expression
[tex]tan(x)csc(c) = \frac{1}{f(x)}\\\frac{sin(x)}{cos(x)} \frac{1}{sin(x)} = \frac{1}{f(x)}\\\frac{1}{cos(x)} = \frac{1}{f(x)}[/tex]
Cross multiply
[tex]cos(x) = f(x)\\Swap\\f(x) = cos(x)[/tex]
in the diagram below given that XY = 30cm, XZY =30° and YZ = x, is it possible to solve for x using the theoram of pythagoras
Answer:
No, you need to know another angle to prove that it is a right triangle to use the Pythagorean theorem.
If you did have an additional side length, that needed angle could be calculated and then use the Pythagorean to prove.
Find the length of the arc, s, on a circle of radius r intercepted by a central angle theta. Express the arc length in terms of pi. Then round your answer to two decimal places. Radius, r = 10 inches; Central angle, theta = 45 degrees
Answer:
arc = 2.5π
Step-by-step explanation:
the circumference of the circle is:
2(10)(π) = 20π
45°/360° = 1/8
(1/8)20π = 2.5π
WILL MARK BRAINLIEST
The number of students in 10 kindergarten classes is shown below
20, 18, 21, 18, 22, 24, 18, 23, 23, 24,
What is the median number of students in the kindergarten classes?
What number of students describes the first quartile
what number of students describes the third quartile
what number of students describes the interquartile range
22 (what number is in the middle one you put it in ascending order)
18 (the first quartile is the first quarter of the sorted list)
23 (the third quarter, the number in between the last number and the median)
5 (the range between quartile 1 and quartile 3)
Have a great day <3
Consider the point on the polar graph below.
Represent the point's location in the polar form (r,θ) where 0≤r<50 and 0≤θ<2π.
(r,θ)=
Represent the point's location in the polar form (r,θ) where 0≤r<50and 2π≤θ<4π.
(r,θ)=
Represent the point's location in the polar form (r,θ) where 0≤r<50and −2π≤θ<0.
(r,θ)=
J0IN G00GLE MEET GIRL$
wnp-hxru-ipf
A construction crew is lengthening a road that originally measured 44 miles. The crew is adding 1 mile to the road each day. The length, L (in miles), after d days of construction is given by the following function.
L(d)= 44+d
What is the length of the road after 35 days?
Answer:
The length of the road after 35 days is of 79 miles.
Step-by-step explanation:
The length of the road, after d days, is given by:
[tex]L(d) = 44 + d[/tex]
What is the length of the road after 35 days?
This is l when d = 35. So
[tex]L(35) = 44 + 35 = 79[/tex]
The length of the road after 35 days is of 79 miles.
In 1 month it rained 12 inches. Then it rained 3 inches per month for 9 months. How many inches did it rain in all?
Answer: 39
Step-by-step explanation: Just addition
Answer:
Total rainfall = 39 inches.
Step-by-step explanation:
The question is not properly qualified. I am assuming that the first month, 12 inches of rain fell (that is an awful lot) and for the next 9 months the rainfall was 3 inches per month.
Let R be the total rainfall.
R = first month + 9*3
R = 12 + 27
R = 39
Need answer asap, correct answer gets brainliest.
Answer:
A is (6,-4)
Step-by-step explanation:
Please help! What is the Area of the Triangle?
Answer and explanation please! <3
Answer:
area of a triangle is equals to sum of all side
Answer:
5√5
Step-by-step explanation:
the area of the triangle is, "base len x height"
the base in here is √1^2 + 2^2 = √5
its height is √4^2 + 3^2 = 5
so the area is √5 x 5 = 5√5
Find the value of x
Answer:
x=80
Step-by-step explanation:
(x+30)=110 because they are vertically opposite angles.
x+30=110
x=110-30
x=80
Answer:
x = 80 degrees
Step-by-step explanation:
x + 30 = 110
- 30 = -30
x = 80 degrees
Use Guauss-jordan elimination to solve the following linear system:
-3x + 4y = -6
5x - y = 10
5 times a number plus 4
Answer:
29
Step-by-step explanation:
5 x 5+4
=25+4 =29
A store gives customers a markup of 13%. If the store sells a belt for $25, what was the wholesale price paid for the belt by the store?
Answer:
$22.12
Step-by-step explanation:
Let x be the wholesale price (the price before adding the markup).
The markup is 13%, so 13% of x is added to x.
x + 13%x = $25
x + 0.13x = 25
1.13x = 25
x = 25/1.13
x = 22.12
Need answer asap, correct answer will get brainliest.
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: A) (2, 4)
Explanation:
the rule is (x,y) --> (x,-y) For reflecting over the x axis
(2,-4) --> (2, 4)
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer:
(2,4)
Step-by-step explanation:
The coordinate of A is (2,-4) currently. If we reflect that point over the x-axis, the y coordinate will change into the opposite sign. Because the y coordinate is -4, it will change to - (-4) = 4. Therefore, the coordinate of A' would be (2,4).
What is the nth term of 60, 110, 160?
Answer and Step-by-step explanation:
The pattern increases by 50 each time.
So, it would be 50n + 60.
#teamtrees #PAW (Plant And Water)
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 421 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 413 grams with a standard deviation of 24. Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
The p-value is approximately 0.0508
Step-by-step explanation:
The given parameters are;
The expected mass of banana chips bag filled by the machine, μ = 421 gams
The number of bags in the sample of bags filled by the machine, n = 26 bags
The mean mass of the bags in the sample, [tex]\overline x[/tex] = 413 grams
The standard deviation of the mass in the bags, s = 24 grams
The level of significance, α = 0.02
The null hypothesis, H₀; μ = 421 grams
The alternative hypothesis, Hₐ; μ < 421 grams
The test statistic is given as follows;
[tex]t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}[/tex]
We get;
[tex]t=\dfrac{413-421 }{\dfrac{24}{\sqrt{26}}} \approx -1.6996731712[/tex]
The t-value = -1.6996731712
The degrees of freedom df = n - 1 = 26 - 1 = 25
From an online source, we get the critical-t = 2.166587
The p-value is obtained using an online source as p(t ≤ -1.6996731712) = 0.0508
From the p-value table, we get
0.05 < p < 0.1
What makes a circle a special kind of geometric figure?
Answer:
it is unlike other shapes
Step-by-step explanation:
it has no egdes,vertices etc.
the ratio of the age of father and his son is 9:4. if the son is 24 years old find the age of father
Answer:
The father is 54 years old
Step-by-step explanation:
Well from the ratio 9:4
We know the son is 24
we can divide 24/4 to get 6
now we know we have to multiply by 6 on each side of the ratio to get the final result
54:24
Answer:
54 years old
Step-by-step explanation:
Because the son is 24 years old, we know that that is 6 times the '4' in the ratio 9:4 therefore if we do 6*9=54 that is the age of his father!
What’s the answer?
What’s the answer?
What’s the answer? What’s the answer? What’s the answer?
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: m<B = 78.4
m<C= 101.6
Explanation:
180 - 78.4 = 101.6
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Find the slope of the line.
Answer:
1/3 is the slope
Step-by-step explanation:
hope this helps
please help i need a fast answer
bhai questions kya hai
than I question of answer
PLEASE HELP ;(
If x varies directly as y, find
x when y = 8.
x = 11 when y = -3
X =
Answer:
1638 or 1368!
Step-by-step explanation:
according to the Michigan DNR, the wolf population on Beaver Island can be modeled by the equation P= 1300(.87)^x. Is the population increasing or decreasing, and by what percent?
Answer:
The population is decreasing by 13%.
Step-by-step explanation:
The standard exponential equation can be modeled by:
y = A(1 ± r)^x
13. Find 3 fractions that are equivalent to 2/3. Explain how you found your answers
Answer:
[tex]\frac{4}{6} =\frac{6}{9}= \frac{8}{12}[/tex]
Step-by-step explanation:
I'm assuming this is asking for 3 separate fractions that are each equal to 2/3
Remember, multiplying the top and bottom of a fraction by a number will not change the fraction.
[tex]\frac{2}{3} *\frac{2}{2} =\frac{4}{6}[/tex]
[tex]\frac{2}{3} *\frac{3}{3} =\frac{6}{9}[/tex]
[tex]\frac{2}{3} *\frac{4}{4} =\frac{8}{12}[/tex]
These three fractions are all equal to 2/3
A cell phone provider classifies its customers as Low users (less than 400 minutesper month) or High users (400 or more minutes per month). Studies have shownthat 80% of the people who were Low users one month will be Low users the nextmonth, and that 70% of the people who were High users one month will be Highusers the next month.
(a) Set up the 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions
(b) Suppose that, during the month of January, 50% of the customers were Low users. What percent of the customers will be Low users in February? In March? (Type an integer or decimal for each matrix element.)
1. The stochastic matrix for the given transitions is:
[tex]T = \left[\begin{array}{ccc}0.80 & 0.20\\0.30&0.70 \end{array}\right]\\[/tex]
2. 40.0% people in February and 32.0% people in March will be the low users if there are 50% low users in January.
It is given that,
80% of the people who were Low users one month will be Low users the next month.
That means for the transition low-low (L-L)
p = 0.80
So, for Low-high transition (L-H)
p = 1-0.80 = 0.20
It is also given that 70% of the people who were High users one month will be High users the next month.
That means, p = 0.70 for the transition high-high (H-H)
Then for H-L transition, p = 1-0.70 = 0.30
(a) The 2x2 stochastic matrix for these transitions is:
[tex]T = \left[\begin{array}{ccc}0.80 & 0.20\\0.30&0.70 \end{array}\right]\\[/tex]
(b) Given that 50% users are the low users in month of January.
[tex]\text{Percent of the customers will be Low users in February}= (\text{low users in month of January} \times \text{Probability of L-L transition.}) \times 100\%[/tex]= (0.50 x 0.80)x100%
= 0.4x 100%
=40.0%
Now, the percentage of people who will be low users in the month of march = (low users in February x probability of L-L transition)x100%
=(0.40x0.80)x100%
=0.32x100%
=32.0%
Hence, the percentage of people who will be low users in the month of February and in the month of March are 40.0% and 32.0% respectively.
Therefore, the results are:
1.2x2 stochastic matrix for the transitions is as:
[tex]T = \left[\begin{array}{ccc}0.80 & 0.20\\0.30&0.70 \end{array}\right]\\[/tex]
2. The percentage of people who will be low users in the month of February and in the month of March are 40.0% and 32.0% respectively.
Learn more about stochastic matrix here:
https://brainly.com/question/29737056
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Can you help me, please?
Answer:
The first one is two over four
Step-by-step explanation: